A study of drop breakage in lean dispersions using the inverse-problem method

Chemical Engineering Science

Volumn 65, Issue 11, 2010, Pages 3681-3694

  O'Rourke, Alan M ^a   MacLoughlin, P F ^a  

^a UNIVERSITY COLLEGE DUBLIN   (Ireland)

Author keywords

Drop breakage; Inverse problem; Liquid liquid dispersions; Population balance; Size distributions; Stirred tank

Indexed keywords

AGITATION CONDITIONS; AVERAGE ENERGY DISSIPATION; BREAKAGE KERNEL; BREAKAGE PROCESS; CONSTANT FACTORS; DIFFERENT SCALE; DISPERSED PHASE; DROP SIZE DISTRIBUTION; ENERGY DISSIPATION RATE; EXPERIMENTAL CONDITIONS; EXPERIMENTAL MEASUREMENTS; FRAGMENT DISTRIBUTIONS; FUNCTION PARAMETERS; GENERALISED FUNCTION; ILL-CONDITIONED; INVERSION METHODS; INVERSION PROCESS; KERNEL FUNCTION; LIQUID-LIQUID DISPERSIONS; PHASE VISCOSITY; POPULATION BALANCE; POPULATION BALANCE EQUATION; POPULATION BALANCES; SELF-SIMILARITIES; SILICONE OIL; STIRRED TANK; VESSEL SIZE;

DENSITY MEASUREMENT (SPECIFIC GRAVITY); DROP FORMATION; ELECTRON ENERGY LOSS SPECTROSCOPY; ENERGY DISSIPATION; ENERGY DISSIPATORS; INVERSE PROBLEMS; LIQUIDS; SILICONES; SIZE DETERMINATION; SIZE DISTRIBUTION; TANKS (CONTAINERS); VISCOSITY;

DISPERSIONS;

EID: 77951099006     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2010.03.003     Document Type: Article

References (50)

1. Alopaeus V., Koskinen J., and Keskinen K.I. Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. Part 1 description and qualitative validation of the model. Chemical Engineering Science 54 (1999) 5887-5899
2. Andersson R., and Andersson B. Modeling the breakup of fluid particles in turbulent flows. A.I.Ch.E. Journal 52 (2006) 2031-2038
3. Andersson R., and Andersson B. On the breakup of fluid particles in turbulent flows. A.I.Ch.E. Journal 52 (2006) 2020-2030
4. Bäbler M.U., Morbidelli M., and Baldyga J. Modelling the breakup of solid aggregates in turbulent flows. Journal of Fluid Mechanics 612 (2008) 261-289
5. Baldyga J., and Bourne J.R. Interpretation of turbulent mixing using fractals and multifractals. Chemical Engineering Science 50 (1995) 381-400
6. Baldyga J., and Podgórska W. Drop break-up in intermittent turbulence: maximum stable and transient sizes of drops. Canadian Journal of Chemical Engineering 76 (1998) 456-470
7. Baldyga J., Bourne J.R., Pacek A.W., Amanullah A., and Nienow A.W. Effects of agitation and scale-up on drop size in turbulent dispersions: allowance for intermittency. Chemical Engineering Science 56 (2001) 3377-3385
8. Bujalski W., Nienow A.W., Chatwin S., and Cooke M. The dependency on scale of power numbers of Rushton disc turbines. Chemical Engineering Science 42 (1987) 317-326
9. Coulaloglou C.A., and Tavlarides L.L. Description of interaction processes in agitated liquid-liquid dispersions. Chemical Engineering Science 32 (1977) 1289-1297
10. Diemer R.B., and Olson J.H. A moment methodology for coagulation and breakage problems: part 3-generalized daughter distribution functions. Chemical Engineering Science 57 (2002) 4187-4198
11. Ducci A., and Yianneskis M. Direct determination of energy dissipation in stirred vessels with two-point LDA. A.I.Ch.E. Journal 51 (2005) 2133-2149
12. Eastwood C.D., Armi L., and Lasheras C.A. The breakup of immiscible fluids in turbulent flows. Journal of Fluid Mechanics 502 (2004) 309-333
13. Galinat S., Masbernat O., Guiraud P., Dalmazzone C., and Noik C. Drop break-up in turbulent pipe flow downstream of a restriction. Chemical Engineering Science 60 (2005) 6511-6528
14. Galinat S., Garrido Torres L., Masbernat O., Guiraud P., Risso F., Dalmazzone C., and Noik C. Breakup of a drop in a liquid-liquid pipe flow through an orifice. A.I.Ch.E. Journal 53 (2007) 56-68
15. Hagesaether L., Jacobsen H., and Svendsen H.F. A model for turbulent binary breakup of dispersed fluid particles. Chemical Engineering Science 57 (2002) 3251-3267
16. Hill P.J., and Ng K.M. Statistics of multiple particle breakage. A.I.Ch.E. Journal 42 (1996) 1600-1611
17. Konno M., Matsunaga Y., Arai K., and Saito S. Simulation model for breakup process in an agitated tank. Journal of Chemical Engineering of Japan 13 (1980) 67-73
18. Konno M., Arai K.A., and Saito . Scale effect on breakup process in liquid-liquid agitated tanks. Journal of Chemical Engineering of Japan 16 (1983) 312-319
19. Kostoglou M., Dovas S., and Karabelas A.J. On the steady-state size distribution of dispersions in breakage processes. Chemical Engineering Science 52 (1997) 1285-1299
20. Kostoglou M., and Karabelas A.J. On the attainment of steady state in turbulent pipe flow of dilute dispersions. Chemical Engineering Science 53 (1998) 505-513
21. Kostoglou M., and Karabelas A.J. A contribution towards predicting the evolution of droplet size distribution in flowing dilute liquid/liquid dispersions. Chemical Engineering Science 56 (2001) 4283-4292
22. Kostoglou M., and Karabelas A.J. Toward a unified framework for the derivation of breakage functions based on the statistical theory of turbulence. Chemical Engineering Science 60 (2005) 6584-6595
23. Kostoglou M., and Karabelas A.J. On the self-similar solution of fragmentation equation: numerical evaluation with implications for the inverse problem. Journal of Colloid and Interface Science 284 (2005) 571-581
24. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chemical Engineering Science 51 (1996) 1311-1332
25. Kuriyama M., Ono H., Takanai H., and Konno H. The number of daughter drops formed per breakup of a highly viscous mother drop in turbulent flow. Journal of Chemical Engineering of Japan 28 (1995) 477-479
26. Lam A., Sathyagal A.N., Kumar S., and Ramkrishna D. Maximum stable drop diameter in stirred dispersions. A.I.Ch.E. Journal 42 (1996) 1547-1552
27. Lasheras J.C., Eastwood C., Martinez-Bazan C., and Montanes J.L. A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow. International Journal of Multiphase Flow 28 (2002) 247-278
28. Luo H., and Svendsen H.F. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42 (1996) 1225-1233
29. Martinez-Bazan C., Montanes J.L., and Lasheras J.C. On the breakup of an air bubble injected into a fully developed turbulent: part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics 401 (1999) 183-207
30. Meneveau C.M., and Sreenivasan K.R. The multifractal nature of turbulent energy dissipation. Journal of Fluid Mechanics 224 (1991) 429-484
31. Narsimhan G., Ramkrishna D., and Gupta J.P. Analysis of drop size distributions in lean liquid-liquid dispersions. A.I.Ch.E. Journal 26 (1980) 991-999
32. Narsimhan G., Nejfelt G., and Ramkrishna D. Breakage functions for droplets in agitated liquid-liquid dispersions. A.I.Ch.E. Journal 30 (1984) 457-467
33. Nere N.K., and Ramkrishna D. Evolution of drop size distributions in fully developed turbulent pipe flow of a liquid-liquid dispersion by breakage. Industrial and Engineering Chemistry Research 44 (2005) 1187-1193
34. O'Rourke A.M., and MacLoughlin P.F. A comparison of measurement techniques used in the analysis of evolving liquid-liquid dispersions. Chemical Engineering and Processing 44 (2005) 885-894
35. Ozisik M.N., and Orlande H.R.B. Inverse Heat Transfer: Fundamentals and Applications (2000), Taylor and Francis, New York
36. Podgórska W. Modelling of high viscosity drop breakage process in intermittent turbulence. Chemical Engineering Science 61 (2006) 2986-2993
37. Podgórska W., and Baldyga J. Scale-up effects on the drop size distribution of liquid-liquid dispersions in agitated vessels. Chemical Engineering Science 56 (2001) 741-746
38. Ramkrishna D. Population Balances (2000), Academic Press, New York
39. Raikar N.B., Bhatia S.R., Malone M.F., and Henson M.A. Self-similar inverse population balance modeling for turbulently prepared batch emulsions: sensitivity to measurement errors. Chemical Engineering Science 61 (2006) 7421-7435
40. Sathyagal, A.N., 1994. Self-similarity in drop breakup phenomena in liquid-liquid dispersions. Identification of break-up functions by inverse problem approach. Ph.D. Thesis, Purdue University.
41. Sathyagal A.N., Ramkrishna D., and Narsimhan G. Solution of inverse problems in population balances-II particle breakup. Computers in Chemical Engineering 19 (1995) 437-451
42. Sathyagal A.N., Ramkrishna D., and Narsimhan G. Droplet breakage in stirred dispersions. Breakage functions from experimental drop-size distributions. Chemical Engineering Science 51 (1996) 1377-1391
43. Silverman B.W. Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall, London
44. Tsouris C., and Tavlarides L.L. Breakage and coalescence models for drops in turbulent dispersions. A.I.Ch.E. Journal 40 (1994) 395-406
45. Vassileva N.D., van den Ende D., Mugele F., and Mellema J. Fragmentation and erosion of two-dimensional aggregates in shear flow. Langmuir 23 (2007) 2352-2361
46. Verhoff F.H., Ross S.L., and Curl R.L. Breakage and coalescence processes in an agitated dispersion. Experimental system and data reduction. Industrial and Engineering Chemistry Fundamentals 16 (1977) 371-377
47. Wang T., Wang J., and Jin Y. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science 58 (2003) 4629-4637
48. Zaccone A., Gabler A., Maas S., Marchisio D., and Kraume M. Drop breakage in liquid-liquid stirred dispersions: modelling of single drop breakage. Chemical Engineering Science 62 (2007) 6297-6307
49. Zaccone A., Soos M., Lattuada M., Wu H., Babler M.U., and Morbidelli M. Breakup of dense colloidal aggregates under hydrodynamic stresses. Physical Review E 79 (2009) 061401.1-061401.6
50. Zhou G., and Kresta S.M. Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank. Chemical Engineering Science 53 (1998) 2063-2079